
Signal: in these simulated data, the true piecewise
constant signal \(\mathbf {m}\)  is available, so an efficient model
selection procedure [1]} would select the
estimated model which is closest to the true signal. That idea is
illustrated in Figure REF , and can be
used in this context by minimizing
\(E_{\text{signal}}(k) = \log _{10}\left[\frac{1}{d} \sum _{i=1}^d(\mathbf {\hat{y}}_i^k - \mathbf {m}_i)^2\right].\) 

In Figure REF , for the
signal sampled at 7 bases/probe, the minimum of the Signal error
identifies a model with 7 segments.

For the signal sampled at 374 bases/probe, the minimum of the
error identifies a model with only 5 segments.


Breakpoint: in these simulated data, the true
breakpoints \(B\)  are available, so we can compute and minimize the
breakpointError as a consistent model selection procedure
[1]}. For both signals, the minimum of the
breakpointError identifies a model with 7 segments (6
breakpoints).

Annotation: we use a set of annotated regions to
compute the incomplete annotation error, which also identifies a
model with 7 segments. It is clear that the annotation error is a
good approximation of the breakpointError. In the next section, we
explicitly demonstrate the link between the breakpointError and the
annotation error.

<FIGURE>